To find the 35th term of an arithmetic sequence, we first need to determine the common difference. The general formula for the nth term of an arithmetic sequence is given by:
an = a1 + (n – 1) * d
where:
- an is the nth term,
- a1 is the first term,
- d is the common difference,
- n is the term number.
Given that:
- a1 = 7
- a18 = 95
We can substitute these values into the formula for the 18th term:
a18 = a1 + (18 – 1) * d
Now, substituting the known values:
95 = 7 + 17d
To find d, we simplify this equation:
95 – 7 = 17d
88 = 17d
Now, dividing both sides by 17 gives:
d = 88 / 17 = 5.1765 (approximately)
Now that we have the common difference, we can find the 35th term:
a35 = a1 + (35 – 1) * d
Substituting the values we have:
a35 = 7 + 34 * (88 / 17)
Calculating this:
a35 = 7 + 34 * 5.1765
a35 = 7 + 176.0 = 183.0
Therefore, the 35th term of the arithmetic sequence is 183.